In general, linear equations have one solution. However, they can have infinitely many solutions in some cases.
A linear equation in mathematics is an equation that can be written in the form
ax + b = 0
The values of x that make this equation true are the solutions to the equation. Generally speaking, linear equations have one solution, which means that there is only one value of x that will make the equation true. However, in some cases, linear equations can have infinitely many solutions. For example, if a = 0 and b = 0, then any value of x will make the equation true.
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Kaylee is going to a carnival that has games and rides. Each game costs
$1.25 and each ride costs $2.50. Kaylee spent $12.50 altogether at the
carnival and the number of rides she went on is twice the number of
games she played. Graphically solve a system of equations in order to
determine the number of games Kaylee played, x, and the number of
rides Kaylee went on, y.
Based on the graph, a solution for the system of equations is 2 and 4.
The number of games Kaylee played is equal to 2 games.The number of rides Kaylee went on is equal to 4 rides.How to write and solve the system of equations graphically?In order to write a system of linear equations to describe this situation, we would assign variables to the number of games Kaylee played and number of rides Kaylee went on, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of games Kaylee played.Let the variable y represent the number of rides Kaylee went on.Since each game costs $1.25 and each ride costs $2.50, and Kaylee spent $12.50 altogether, we have;
1.25x + 2.50y = 12.50. ..........equation 1.
Additionally, the number of rides she went on is twice the number of
games she played;
y = 2x ..........equation 2.
Next, we would use an online graphing calculator to graphically solve the system of linear equations. Therefore, the required solution for the given system of linear equations is the point of intersection of the two (2) lines on the graph, which is given by this coordinate (2, 4).
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6.Which of these statements is correct? Select all that apply.
Responses
the built-in math function is square root or cube root.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
The correct options are:
A solution to the equation x2=81 is x=9.
A solution to the equation x3=125 is x=5.
A solution to the equation x3=216 is x=6.
Hence the built-in math function is square root or cube root.
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There are 24 members of a kayaking club this summer. Next year, Owen hopes the number of members will be 125% of this number.
Write a percent equation in the form part = percent • whole that can be used to find 125% of 24. Use p to represent the part and represent the percent as a decimal.
The percent equation in the form of p = percent x whole is
p = 1.25 x 24
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of members in the club = 24
Number of members in the club next year = 125% of 24
The percent equation of 125% of 24.
p = 125/100 x 24
p = 1.25 x 24
p = 5/4 x 24
p = 5 x 6
p = 30
Thus,
The percent equation is p = 1.25 x 24
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the measure of ∠1 is 50 degrees. what is the measure of ∠6 ?
If the measure of angle 1 is 50° then the measure of angle 2 is 30°.
We know that line l ∥ line m and line p is the transversal.
Let's label the diagram as follows.
Now, by the vertically opposite angles theorem,
we have angle 1 = ∠TPQ = 50°
now ∠P and ∠Q form interior angles,
Hence, by the interior angles theorem, we have
∠P + ∠Q = 180°
The sum of the interior angles of the angles formed by the transversal is 180°.
50° + ∠Q = 180°
subtracting 50° on both sides we get,
∠Q = 180° - 50°
∠Q = 30°
Hence, the measure of angle 2 is 30°.
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The complete question is -
In the given figure, line l and line m are parallel and line p is transversal If the measure of 1 is 50 degrees what is the measure of 2?
Find the value of X
(Please help)
Answer: x = 19
Step-by-step explanation:
Let's start with what we know. The area of a trapezoid is:
(B1 + x) * H /2 = Area
So here we have:
(25 + x)* 7 /2 = 154.
We multiply by 2 on both sides:
(25 + x)*7 = 308
Divide by 7 on both sides:
25 + x = 44
Subtract 25 from both sides:
x = 19.
So x = 19.
Answer: 19 inches
Step-by-step explanation:
The shape is a trapezium. (You can tell as there is one pair of parallel sides.) Therefore, to find the area, the following formula is needed:
Area of a trapezium = [tex]\frac{a + b}{2} * h[/tex]
a and b represent the parallel sides
Next, plug in the given values:
[tex]154 = \frac{x + 25}{2} * 7[/tex]
Rearrange the equation to get x on its own:
[tex]154 = \frac{x+25}{2} * 7\\\\\frac{154}{7} = \frac{x+25}{2} \\\\22 = \frac{x+25}{2} \\\\22*2 = x + 25\\\\44 = x + 25\\\\44-25 = x\\\\x = 19\\\\[/tex]
Therefore, the answer is 19 inches. Remember your units!
what is the difference between descriptive statistics and inferential statistics?
A data set's attributes are enumerated through descriptive statistics. You can use inferential statistics to test a hypothesis or determine whether your data can be applied to a larger population.
Descriptive statistics concentrate on describing the features of a dataset that are readily evident (a population or sample). In contrast, inferential statistics concentrate on drawing conclusions or generalisations from a sample of data in a larger dataset.
The information from a research sample is described and condensed using descriptive statistics. We can draw conclusions about the larger population from which we drew our sample using inferential statistics.
The area of statistics known as descriptive statistics is focused on providing a description of the population being studied. A type of statistics known as inferential statistics concentrates on inferring information about the population from sample analysis and observation.
Hence we get the required answer.
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A shoe company packs boxes of shoes in crates, divide to complete the table
Answer:
2/ 95
3/ 72
4/ 453
Step-by-step explanation:
2/ Take 2185 divided by 23 = 95
3/ Take 3888 divided by 54 = 72
4/ Take 7248 divided by 16 = 453
Identifying Products Resulting in a Sum or Difference of
Cubes
Sum of cubes:
(a + b)(a²-ab + b²) = a³ + b³
Difference of cubes:
(a-b)(a² + ab + b²)=a³-b³
4) Intro
Which products result in a sum or difference of cubes?
Check all that apply.
(x-4)(x2+4x-16)
□ (x-1)(x²-x+1)
(x-1)(²+x+1)
(x+1)2+x-1)
(x+4)(x²-4x+16)
□ (x+4)(x2 + 4x + 16)
The products result in a sum or difference of cubes are
(x - 1)(x² + x + 1) and (x + 4)(x² - 4x + 16).
What is sum or difference of cubes?
The term "sum of cubes" refers to a polynomial with the formula a^3 + b^3. The term "difference of cubes" refers to a polynomial with the form
a^3 - b^3.
The formulas for sum of cubes and difference of cubes are given:
Sum of cubes: (a + b)(a²-ab + b²) = a³ + b³
Difference of cubes: (a-b)(a² + ab + b²)=a³-b³
We have to check which products result in a sum or difference of cubes.
Consider,
(1) (x - 4)(x^2 + 4x - 16)
(x - 4)(x^2 + 4x - 16) = x^3 - 8x^2 + 32x - 64
It is not a sum or difference of cubes.
(2) (x-1)(x²-x+1)
(x - 1)(x² - x + 1) = x^3 - 2x^2 + 2x - 1
It is not a sum or difference of cubes.
(3) (x - 1)(x² + x + 1)
(x - 1)(x² + x + 1) = x^3 - 1
This is the difference of cubes.
(4) (x + 1)(x^2 + x - 1)
(x + 1)(x^2 + x - 1) = x^3 + 2x^2 - 1
It is not a sum or difference of cubes.
(5) (x + 4)(x² - 4x + 16)
(x + 4)(x² - 4x + 16) = x^3 + 64
This is the sum of cubes.
(6) (x + 4)(x^2 + 4x + 16)
(x + 4)(x^2 + 4x + 16) = x^3 + 8x^2 + 32x + 64
It is not a sum or difference of cubes.
Hence, the products result in a sum or difference of cubes are
(x - 1)(x² + x + 1) and (x + 4)(x² - 4x + 16).
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8,3, -i
what is the polynomial function for these numbers
Answer:
f(x) = x⁴ - 11x³ + 25x² - 11x + 24---------------------------------
It is assumed the provided numbers are the zero's of the polynomial function.
We know complex zero's come in pairs if function has rational constants.
So we should have zero's: 8, 3, -i and i.
Find the polynomial:
f(x) = (x - 8)(x - 3)(x + i)(x - i) = (x² - 11x + 24)(x² + 1) = x⁴ - 11x³ + 25x² - 11x + 24the different geometries that a molecule can attain by bond rotations and bends are called conformations. True/False ?
TRUE: A molecule can adopt a variety of geometries known as conformations by the rotation and bending of its bonds.
Conformational isomerism, often known as stereoisomerism, is a type of stereoisomerism in chemistry in which the isomers can be changed to one another simply by rotations about formally single bonds. Different conformations refer to any two arrangements of atoms in a molecule that differ by rotation about a single bond, whereas conformations that correspond to local minima on the potential energy surface are more specifically known as conformational isomers or conformers.
As a result, conformational isomers differ from other classes of stereoisomers (such as configurational isomers), where interconversion entails the necessary breaking and reformation of chemical bonds.
Thus, the statement, The different geometries that a molecule can attain by bond rotations and bends are called conformations is TRUE
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using the information in q8, what is the optimal number of cookies to make? 2,600 dozen 2,400 dozen 2,200 dozen 2,000 dozen 2,800 dozen
By using probability, it can be calculated that-
the optimal number of cookies to make is 2400 dozens
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Here
Each dozen of cookies is sold for $1.99 and cost $0.99
Shortage = $(1.99 - 0.99) = $1
Cookies that are not sold at the end of the day are reduced to $0.49
Overage = $(0.99 - 0.49) = $0.5
Service = [tex]\frac{1}{1 + 0.5}\\[/tex]
[tex]=\frac{1}{1.5}\\\\=\frac{2}{3}\\\\=0.67[/tex]
Now the table is
Demand Probability of demand Cumulative probability
(Dozen)
1800 0.05 0.05
2000 0.15 0.2
2200 0.2 0.4
2400 0.3 0.7
2600 0.2 0.9
2800 0.1 1
Here the closest to service is 0.7
So the optimal number of cookies to make is 2400 dozens
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Complete Question
Famous Albert prides himself on being the Cookie King of the West. Small, freshly baked cookies are specialty of his shop. Each dozen sells for $1.99 and costs $0.99, which includes handling and transportation. Cookies that are not sold at the end of the day are reduced to $0.49 and sold the following day as day-old merchandise. Famous Albert has asked for help to determine the number of cookies he should make each day. From an analysis of past demand he estimates demand for cookies as
Demand Probability of demand Cumulative probability
(Dozen)
1800 0.05
2000 0.15
2200 0.2
2400 0.3
2600 0.2
2800 0.1
Using the information in q8, what is the optimal number of cookies to make? 2,600 dozen 2,400 dozen 2,200 dozen 2,000 dozen 2,800 dozen
2,600 dozen 2,400 dozen 2,200 dozen 2,000 dozen 2,800 dozen
Write the equation of the line in fully simplified slope-intercept form.
Answer: y = -1/2x - 3
Step-by-step explanation:
What is an example of a function equation?
The example of the function equation is f(x+3) = x² + 8x + 16 .
In the question ,
we have been asked to give an example of the function equation .
The Function Equation is defined as equations where the unknowns are functions, rather than a traditional variable.
For Example :
If f(x+3) = x² + 8x + 16 , then what is f(x)?
the above question is an example of function equation .
to find the solution ,
we let ,y = x + 3; then x = y - 3 .
Substituting the value of x in f(x+3) we get ,
f(y) = 2y² + 2y + 1 .
hence f(x) = 2x² + 2x + 1 that is = (x + 1)² .
Therefore , the example is f(x+3) = x² + 8x + 16 .
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Suppose the odds of rain today are 5:9 What would be the probability that it will rain today?
The probability is the odds thus the probability it will rain today will be 5/9.
What is probability?Probability is the concept that describes the likelihood of an event occurring.
Probability is also known as chance because, if you flip a coin, the possibilities that it will land on its head or tail are just chances that either a head will show up or not.
The odds of rain today are 5:9
Odds will be the same as probability because the probability is the same as chance.
Probability = 5/9
Hence "Since probability equals odds, the likelihood that it will rain today is 5/9.".
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suppose that the rural wage is $2 per day. urban modern sector employment can be obtained with a probability of 0.24 and pays $4 per day. the urban informal sector pays $1 per day. using this information, and making assumptions as needed, predict whether there will be any rural-to-urban or urban-to-rural migration? explain your reasoning, stating explicitly any simplifying assumptions, and show all your work.
The solution to given problem is since E(Wu) < Wr, there will be no migration from rural areas .
What does probability theory entail?
The subject of probability in mathematics is concerned with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, with 1 typically signifying certainty and 0 typically signifying impossibility.
Here,
Since ,the rural wage is $2 per day. Urban modern sector employment can be obtained with .24 probability and pays $4 per day. The urban traditional sector pays $1 per day.
As long as the rural pay (Wr) differs from the anticipated urban wage (E(Wu)), according to the Harris-Todaro model, there will be movement between rural and urban areas.
Here, Wr equals $2.00.
Determine the anticipated urban wage now.
E(Wu) = p
*Wum+(1-p)
*Wut
Where p is the likelihood of finding employment in the urban modern sector, which is 0.25, and Wum is the wage for such employment, which is $4.00.
Wut = $1.00 in wages for jobs in the typical urban sector.
Hence, E(Wu) = 0.24*$4.00+0.76*$1.00 = $1.72
Since E(Wu) < Wr, there will be no migration from rural areas .
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you draw a two-card hand from a standard deck of 52 cards. what is the probability of drawing a hand that contains exactly 2 face cards (a face card is a king, queen, or jack)?
By using the concept of probability, it can be calculated that -
Probability that a two-card hand from a standard deck of 52 cards contains exactly 2 face cards (a face card is a king, queen, or jack) = [tex]\frac{11}{221}[/tex]
What is probability?
At first it is important to know about probability of an event.
Probability gives us the information about how likely an event is going to occur.
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Number of face card = 12
Total number of cards = 52
Probability that a two-card hand from a standard deck of 52 cards contains exactly 2 face cards (a face card is a king, queen, or jack) = [tex]\frac{{12 \choose 2}}{{52 \choose 2}}[/tex]
= [tex]\frac{66}{1326}[/tex]
= [tex]\frac{11}{221}[/tex]
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A `16`-ounce bottle of orange juice contain `200` milligram of vitamin C, which i `250\%` of the daily recommended amount (for adult). What i `100\%` of the daily recommended amount of vitamin C?
If 16 ounce bottle of orange juice contain 200 milligram was 250% from total of daily recommended amount , then 100% or recommended vitamin C to daily consume is 80 milligram.
How to prove it?It was given that in a bottle on 16-ounce bottle size contains 200 milligram of vitamin C, which is contain 250% amount of recommended daily consume. Then to know a real amount or recommended amount to consume vitamin C in daily is: 200/250 × 100.The result from 200/250 × 100, is 80.Then the conclusion is, recommended daily consume of vitamin C, or 100% of the daily recommended amount of vitamin C is, 80 milligram.Learn more about the percentage here: brainly.com/question/2724587
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suppose the estimated regression equation is given by . what are the predicted value of y and the residual when x is 2 and y is observed to be 9?
The predicted value and residual for y is 9.4 and -0.4 respectively.
In statistics, a regression equation is used to determine whether or not there is a relationship between two sets of data. If you measure a child's height every year, you might discover that they grow about 3 inches per year. A regression equation can be used to model that trend (growing three inches per year). In fact, most things in the real world (from gas prices to hurricanes) can be modelled mathematically, allowing us to forecast future events.
Regression equations can assist you in determining whether your data can be fit to an equation. This is extremely useful if you want to make predictions based on your data, whether they are future predictions or indications of past behaviour.
Given,
Regression equation is y=11-038x
Observed value of y = 9
predicted value of y can be determined by substituting x=2 in the equation
y=11-0.8(2)=11-1.6=9.4
The residual can be calculated by formula,
residual = observed value - predicted value
residual = 9 - 9.4
residual = -0.4
Thus, the predicted value is 9.4 and residual is -0.4.
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Your question is incomplete, here is the complete question.
suppose the estimated regression equation is given by y=11-0.8x . what are the predicted value of y and the residual when x is 2 and y is observed to be 9?
the wait time to ride the ferris wheel at a state fair is 15 minutes when 75 people are in line. at this rate, how long is the wait time when 200 people are in line?
The wait time required for 200 people are in line would be 40min.
Given that:
wait time to ride the ferris wheel for 75 people is 15 minutes.
we have given 200 people that are in line to ride.
for each person in line from the beginning is an additional 0.2 wait time.
so, the number of people in line n times = 0.2 = wait time.
Therefore,
[tex]\frac{15\ min}{75 \ people}=0.2\frac{min}{people} \\\\wait \ time = n*0.2\frac{min}{people} \\\\wait\ time = (200)*0.2\frac{min}{people}\\\\wait\ time = 40 min[/tex]
Hence, The wait time required for 200 people are in line would be 40min.
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What is the value of x?
Enter your answer as a decimal to the nearest tenth in the box.
Answer:3
Step-by-step explanation:
Find the number x, If 11/3 of x is 55
The missing number of the algebraic expression is; x = 15
How to solve algebraic word problems?We are given the algebraic expression that we should find the number x, If 11/3 of x is 55.
This can be expressed as;
(11/3)x = 55
Multiply through by 3 to get;
(11/3)x * 3 = 55 * 3
11x = 165
Divide both sides by 11 to get;
11x/11 = 165/11
x = 15
Which we conclude that 15 is the missing number.
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Kaylon shaded the thermometer to represent a temperature of degrees below zero Celsius as shown in the diagram. Is she correct? Therm
Question 5 options:
A: She incorrect because she should have shaded in °
B: She is correct because she shaded a temperature of -°C.
C: She is incorrect because she shaded a temperature of −°
By ay applying logical reasoning, we can conclude that (C) Kaylon is incorrect because the provided image indicates that the shaded temperature is -°.
What is logical reasoning?Induction and abduction are two additional categories of logical reasoning that are typically distinguished in addition to the formal deduction.
If one has a premise or precondition, a conclusion or logical consequence, and a rule or material conditional that signals the conclusion given the premise, one can explain the following.
Philosophical logic and mathematical logic are often used to support the assertion that "Objects outside get wet when it rains.
Since the grass is outside, it gets wet when it rains."
Inductive reasoning is used to support a finding of the rule.
Based on the information provided, it is clear that Kaylon is mistaken because the temperature in the shade is -°.
Therefore, by applying logical reasoning, we can conclude that (C) Kaylon is incorrect because the provided image indicates that the shaded temperature is -°.
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Question 2 Please Help Me!!!
Answer:
option a) since the arcs r drawn on both the sides of the line
and also as the arcs intersect each other at the center of the line AB
can someone pls help me with algebra on number 5
Answer:
first option
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 8 ) and (x₂, y₂ ) = (6, 4 )
m = [tex]\frac{4-8}{6-0}[/tex] = [tex]\frac{-4}{6}[/tex] = - [tex]\frac{2}{3}[/tex]
the line crosses the y- axis at (0, 8 ) ⇒ c = 8 , then
y = - [tex]\frac{2}{3}[/tex] x + 8 ← option 1
What is the range of a function in simple terms?
The group of all possible dependent values that a function can produce from its domain values is known as its range.
In the given question we have to explain what is range of a function.
The range refers to all the entities (output) that result from a relation or function. The Range set is made up of all used output values (dependent values).
The group of all possible dependent values that a function can produce from its domain values is known as its range. It consists of every potential output.
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A study indicated that the citizens of Washington wasted 7,470 gallons of water last year. This year, they wasted 30% less. How many gallons did the citizens waste this year?
The number of gallons the citizens waste this year is 5229
How to find the number of gallonsinformation from the problem
The citizens of Washington wasted 7,470 gallons of water last year
This year, they wasted 30% less
The question is a percentage problem, percentage deals with a fraction hundred and used as follows
30%
= 30 / 100
= 0.3
The factor 0.3 less
= 1 - 0.3 = 0.7
The number of gallons wasted this year
= 0.7 * 7470
= 5229
The number of gallons wasted is 5229 gallons
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Finn shows his work in finding the solution to 4x+6=2+3(x+2). After checking his answer in the original equation, he found that it did not work. Where did he make a mistake?.
Finn had solved the bracket in an incorrect way because of which he got a wrong answer.
Here we see that the equation is
4x + 6 = 2 + 3(x + 2)
Here we see that Finn has opened the brackets to write
4x + 6 = 2 + 3x + 2
Here is the point where he made a mistake.
When we have a term that needs to be multiplied by the terms in a bracket, we need to multiply it with every term inside the bracket.
This means, that 3 needs to be multiplied with x as well as 2.
Hence we get
4x + 6 = 2 + 3x + 6
Now if we deduct 3x from both sides we will get
x + 6 = 8
Now deducting 6 from both sides gives us
x = 2
Hence the value of x is 2
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(7x³ + x² + x) ÷ (x² + 1)
Answer:
7x + 1 Remainder -6x - 1
or
7x + 1 - (6x + 1)/(x² + 1)
Step-by-step explanation:
(7x³ + x² + x) ÷ (x² + 1)
7x + 1
---------------------
x² + 1 | 7x³ + x² + x
7x³ + 0 + 7x
------------------------
x² - 6x
x² + 0x + 1
--------------------
-6x - 1
(7x³ + x² + x) ÷ (x² + 1) = 7x + 1 Remainder -6x - 1
or
(7x³ + x² + x) ÷ (x² + 1) = 7x + 1 - (6x + 1)/(x² + 1)
Which table represents a linear function?
the table:4 represents a linear function.
What is system of linear equations?
The intersections or meetings of the lines or planes that represent the linear equations are known as the solutions of linear equations. The set of values for the variables in every feasible solution is a solution set for a system of linear equations.
Not a Solution
If there is no intersection of any lines, or if the graphs of the linear equations are parallel, then the system of linear equations cannot be solved.
An Endless Number of Options
A set of infinite points exists for which the L.H.S. and R.H.S. of an equation become equal, indicating that a system of linear equations has an infinite number of solutions.
Unique fixing a series of linear equations
For table 4: The slope will be (8-6)/(3-5) = 2/-2 = -1
and (10-8)/(1-3) = 2/-2 = -1
Hence, the table:4 represents a linear function.
For a function to be linear the slope of all the segments should be same.
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a box contains five slips of paper marked $1, $1, $1, $10 and $25. the winner of a contest selects 2 slips of paper at random and gets the larger of the $ amounts on the slips. define the random variable w
The probability when the value of W = 1 is 0.1 , probability when the value of W = 10 is 0.2 and probability when the value of W = 25 is 0.7 .
In the question ,
the marked price slips are $1, $1, $1, $10 and $25 .
If the winner selects two slips of paper, then the possible outcomes would be ,
total number of slips is = 5 ,
Total number of cases possible = ⁵C₂ = 10
There would be only 1 case in which the winner will win $1
that means when both the slips selected has $1.
So, P(Winning $1) = 1/10 = 0.1
the number of cases to win $10 is {(1,10) , (10,1)}
So , P(Winning $10) is
= 2/10 = 0.2
So , P(Winning $25) is
= 1 - (0.1 [tex]+[/tex] 0.2)
= 0.7
Therefore , the required probability P(Winning $1) = 0.1 , P(Winning $10) = 0.2 and P(Winning $25) = 0.7
The given question is incomplete , the complete question is
A box contains five slips of paper, marked $1, $1, $10, $25, and $25. The winner of a contest selects two slips of paper at random and then gets the larger of the dollar amounts on the two slips. Define a random variable w by w = amount awarded. Determine the probability distribution of w. (Hint: Think of the slips as numbered 1, 2, 3, 4, and 5, so that an outcome of the experiment consists of two of these numbers.)
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